Distinct signal strengths, defined as the production rate times the decay branching fraction relative to the SM expectation, i.e., \(\mu _{i} \equiv (\sigma \times \mathrm {BR})_{i} /(\sigma \times \mathrm {BR})_{i}^{\mathrm {SM}}\) , in various decay channels including \(\gamma \gamma \) , \(WW^{\ast }\) , \(ZZ^{\ast }\) , \(b\bar{b}\) , and \(\tau ^+\tau ^-\)  have already been measured with high precision at the LHC.
From these signal strengths, one can obtain information on the couplings of the Higgs boson to SM particles
and derive constraints on the extension models.
For the model considered in this work and in the narrow width approximation, the signal strength of \(\mathcal {H}\)  is [1]}
\(\mu _{\mathcal {H}}=\frac{\Gamma _{\mathcal {H}}^{\mathrm {SM}} \cos ^{4} \theta }{\Gamma _{\mathcal {H}}^{\mathrm {SM}} \cos ^{2}\theta +\Gamma _{\mathcal {H} \rightarrow \chi \chi }+\Gamma _{\mathcal {H} \rightarrow \mathcal {SS}}},\) 
